The adaptive techniques for links are usually performed within the layers

often resulting in the optimization of local performance

but not of the entire system.This paper first presents a cross-layer design scheme for LTE systems by using two adaptive transmission techniques

i.e.Adaptive Modulation and Coding（AMC） at the physical layer and Hybrid Automatic Retransmission Request（HARQ） at the Medium Access Control（MAC） sublayer.Then

it analyzes the relationship between the cross-layer coupling parameters and the system performance and gives a detailed derivation process and a concrete expression.Finally

it formulates the cross-layer optimization under the constraints of the average time delay and packet error rate.Simulation results indicate that the proposed cross-layer design can further improve the average spectral efficiency and select the optimum maximum number of HARQ and way of AMC in line with the channel quality so as to maximize the average spectral efficiency under the specified Quality-of-Service（QoS） requirements.